Consensus control method for second-order multi-agent systems based on extended state observer

Abstract

The present invention discloses a second-order multi-agent system consistency control method based on an extended state observer. First, a second-order multi-agent system model is established, and an extended state observer is designed based on the model to respectively estimate the position, speed and interference of each agent in real time; then, the estimation error is defined, and the design range of the extended state observer parameters is given; then, a multi-agent system consistency control protocol is designed, and the extended state observer and the multi-agent system consistency control protocol are applied to the second-order multi-agent system to perform a performance test; the method provided by the present invention can estimate the speed and interference in real time based on the position information of the system only when the speed information cannot be obtained or the cost of obtaining the speed information is too high, and on this basis, a control law is designed to compensate for the interference, thereby achieving more complex control goals on the basis of satisfying anti-disturbance.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent systems, and mainly to a second-order multi-agent system consistency control method based on an extended state observer. Background Art

[0002] In recent years, collaborative control has attracted more and more attention from the academic community due to its wide application in space exploration, space perception, formation control and other fields. Whether it is an unmanned vehicle, a drone or other entities with autonomous control, they can be regarded as a specific form of intelligent agent. Multi-agent system combines multiple independent agents to form a network system. Compared with a single agent, it has obvious advantages in efficiency, safety, and reliability. The consistency problem in a multi-agent system means that the states of the agents in the system can be consistent. The key to solving the consistency problem is to design a suitable control protocol for each agent. Formation control, cluster control, etc. all need to be designed on the premise of solving the consistency problem. Therefore, solving the consistency problem is the key to the multi-agent system.

[0003] In practical applications, almost all control systems are more or less subject to interference to varying degrees. The presence of interference may not only reduce the control accuracy of the system, but also cause the system to diverge in severe cases. At the same time, since the motion environment of the multi-agent system is more complex and more susceptible to the adverse effects of external interference, it is crucial to study the anti-interference problem of the multi-agent system and improve the robustness and reliability of the system. Summary of the invention

[0004] Purpose of the invention: In view of the problems existing in the above background technology, the present invention provides a second-order multi-agent system consistency control method based on an extended state observer, which realizes the output consistency of the agents on the basis of determining the estimation accuracy. Compared with other forms of disturbance observers, the present invention expands the range of parameter selection and therefore has a wider application prospect.

[0005] Technical solution: To achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A second-order multi-agent system consistency control method based on an extended state observer, characterized in that it comprises the following steps:

[0007] Step S1, establishing a second-order multi-agent system model;

[0008] Step S2, designing an extended state observer based on the second-order multi-agent system model in step S1, and performing real-time estimation of the position, speed and interference of each agent;

[0009] Step S3, defining the estimation error and providing the design range of the extended state observer parameters;

[0010] Step S4, designing a multi-agent system consistency control protocol;

[0011] Step S5: Apply the extended state observer and the multi-agent system consistency control protocol to the second-order multi-agent system model described in step S1 to perform performance testing.

[0012] Furthermore, the second-order multi-agent system model in step S1 is established as follows:

[0013]

[0014]

[0015] where x i (t), v i (t) and d i (t) is the position, speed and external interference of the i-th agent; u i (t) represents the control input of agent i; i∈{1, 2, ..., n} represents the number of agents in the multi-agent system;

[0016] There exists a parameter D such that

[0017] Furthermore, the extended state observer in step S2 is specifically designed as follows:

[0018]

[0019]

[0020]

[0021] in and represents the estimation of the position, velocity and external disturbance of the ith agent, and i∈{1, 2, ..., n}; α 1 , α 2 and α 3 are the parameters of the extended state observer respectively; for the scalar x, sgn(x) represents the sign function, as follows:

[0022]

[0023] where sig r (x) = sgn(x) |x| r , r is a constant.

[0024] Furthermore, the parameter design method of the extended state observer in step S3 is specifically as follows:

[0025] The definition of estimation error is as follows:

[0026]

[0027]

[0028]

[0029] The Lyapunov function is designed as follows:

[0030]

[0031] in To satisfy the positive condition,

[0032] p 11 >0

[0033]

[0034]

[0035] Extended state observer parameter α 1 , α 2 and α 3 The extended state observer can estimate the agent when the following conditions are met:

[0036] P 1 <0

[0037] k<0

[0038] α 1 , α 2 , α 3 >0

[0039] α 1 p 11 +2α 2 p 12 -2kp 13 >0

[0040] 4(α 1 p 11 +2α 2 p 12 -2kp 13 ) 12 +(p 11 -α 1 p 13 -2α 2 p 22 +2kp 23 )2 <0

[0041]

[0042] At the same time, the position estimation error satisfies in

[0043]

[0044]

[0045] Furthermore, the consistency control protocol designed in step S4 is as follows:

[0046]

[0047] where u(t)=[u 1 (t), ..., u n (t)] T , x(t)=[x 1 (t), ..., x n (t)] T , v(t)=[v 1 (t), ..., v n (t)] T , L is the Laplace matrix of the multi-agent system, which represents the communication relationship between agents. The specific expression is as follows:

[0048]

[0049] where a ij is an element of the adjacency matrix A; when agent i can send information to agent j, then a ij =1, otherwise a ij =0.

[0050] Furthermore, in step S5, a test is performed based on a MATLAB / SIMULINK simulation platform to obtain position and speed change curves in the multi-agent system, and the curves are compared with those without the use of an extended state observer to verify system performance.

[0051] Beneficial effects:

[0052] The extended state observer designed by the present invention can make real-time estimates of speed and disturbance based on the position information of the system only when the speed information cannot be obtained or the cost of obtaining the speed information is too high, and design a control law to compensate for the disturbance on this basis, so as to achieve more complex control objectives on the basis of satisfying the anti-disturbance. On the one hand, the position, speed and disturbance estimation errors can be controlled within a bounded range; on the other hand, the designed control law can make the system generalize to a wider range of applications while satisfying the consistency. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a flow chart of the second-order multi-agent system consistency control method based on the extended state observer of the present invention;

[0054] Figure 2 It is the network topology diagram of the second-order multi-agent system;

[0055] Figure 3 The position and velocity change curve of the multi-agent system without using the extended state observer;

[0056] Figure 4 This is the position and velocity change curve of the multi-agent system based on the extended state observer. DETAILED DESCRIPTION

[0057] The present invention is further described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] The second-order multi-agent system consistency control method based on extended state observer provided by the present invention is as follows Figure 1 As shown, the following steps are included:

[0059] Step S1: Establish a second-order multi-agent system model as follows:

[0060]

[0061]

[0062] where x i (t), v i (t) and d i (t) are the position, velocity and external disturbance of the ith agent. i (t) represents the control input of agent i. i∈{1, 2, ..., n} represents the number of agents in the multi-agent system.

[0063] There exists a parameter D such that

[0064] The second-order multi-agent system is a system composed of multiple agents mentioned above. The agents communicate with each other according to established rules to transmit each other's position, speed information, etc.

[0065] Step S2: Design an extended state observer based on the second-order multi-agent system model in step S1 to estimate the position, speed and interference of each agent in real time.

[0066] The specific design of the extended state observer is as follows:

[0067]

[0068]

[0069]

[0070] in and represents the estimation of the position, velocity and external disturbance of the i-th agent, and i∈{1, 2, ..., n}. 1 , α 2 and α 3 are the parameters of the extended state observer. For a scalar x, sgn(x) represents a sign function, as follows:

[0071]

[0072] where sig r (x) = sgn(x) |x| r , r is a constant.

[0073] Step S3: define the estimation error and give the design range of the extended state observer parameters.

[0074] The definition of estimation error is as follows:

[0075]

[0076]

[0077]

[0078] The Lyapunov function is designed as follows:

[0079]

[0080] in To satisfy the positive condition,

[0081] p11 >0

[0082]

[0083]

[0084] Extended state observer parameter α 1 , α 2 and α 3 The extended state observer can estimate the agent when the following conditions are met:

[0085] P 1 <0

[0086] k<0

[0087] α 1 , α 2 , α 3 >0

[0088] α 1 p 11 +2α 2 p 12 -2kp 13 >0

[0089] 4(α 1 p 11 +2α 2 p 12 -2kp 13 ) 12 +(p 11 -α 1 p 13 -2α 2 p 22 +2kp 23 ) 2 <0

[0090]

[0091] At the same time, the position estimation error satisfies in

[0092]

[0093]

[0094] Step S4: Design the multi-agent system consistency control protocol as follows:

[0095]

[0096] where u(t)=[u 1 (t), ..., u n (t)]T , x(t)=[x 1 (t), ..., x n (t)] T , v(t)=[v 1 (t), ..., v n (t)] T , L is the Laplace matrix of the multi-agent system, which represents the communication relationship between agents. The specific expression is as follows:

[0097]

[0098] where a ij is an element of the adjacency matrix A. When agent i can send information to agent j, then a ij =1, otherwise a ij =0.

[0099] Step S5: Apply the extended state observer and the multi-agent system consistency control protocol to the second-order multi-agent system model in step S1 to perform performance testing.

[0100] The present invention is tested based on the MATLAB / SIMULINK simulation platform to obtain the position and speed change curves in the multi-agent system, and compares them with the change curves without the extended state observer to verify the consistency control method of the second-order multi-agent system based on the extended state observer of the present invention. The following is a specific embodiment:

[0101] The designed extended state observer is applied to the second-order multi-agent system model built in step 1 and tested on the MATLAB / SIMULINK simulation platform. This embodiment adopts a system composed of 5 second-order agents, whose network topology is as follows: Figure 2 As shown, the circles represent agents, and the straight lines between them represent communication relationships. Here, the initial states of the five agents are set to x(0) = [60, 55, 35, 75, 40] T and v(0) = [2.5, 4.5, 6, 2, 6.5] T .Depend on Figure 2 The Laplace matrix of the network can be obtained as

[0102]

[0103] Set the external disturbance of the five agents to

[0104] d 1 (t) = sin(2t) + cos(t)

[0105] d 2(t) = cos(t) - sin(2t)

[0106] d 3 (t) = 2sin(t)

[0107] d 4 (t) = sin(3t) + 0.5

[0108] d 5 (t) = sin(t) - 2cos(t)

[0109] Depend on Figure 3 It can be seen that when the extended state observer is not used, the position and speed of the system cannot converge to the same value. Although each agent tends to approach each other compared to the initial state, they cannot reach the same value over time. Figure 4 As shown in the figure, after using the extended state observer, the problem has been significantly improved. The position (left figure) and speed (right figure) of the system have reached consistency in about 15s, and then the consensus speed of the system is maintained at about 5m / s, that is, the control target of consistency is achieved. Therefore, the extended state observer and consistency control protocol designed by the present invention effectively weaken the impact of interference on the system, improve the anti-interference ability and robustness of the system, and have good engineering application value.

[0110] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A second-order multi-agent system consensus control method based on an extended state observer, characterized in that: The following steps are involved: Step S1, establishing a second-order multi-agent system model; Step S2, designing an extended state observer based on the second-order multi-agent system model in step S1, and performing real-time estimation of the position, speed and interference of each agent; Step S3, defining the estimation error and providing the design range of the extended state observer parameters; Step S4, designing a multi-agent system consistency control protocol; Step S5, applying the extended state observer and the multi-agent system consistency control protocol to the second-order multi-agent system model in step S1 to perform performance testing; The second-order multi-agent system model in step S1 is established as follows: where x i (t), v i (t) and d i (t) is the position, speed and external interference of the i-th agent; u i (t) represents the control input of agent i; i∈{1,2,…,n} represents the number of agents in the multi-agent system; There exists a parameter D such that The extended state observer in step S2 is specifically designed as follows: in and represents the estimation of the position, velocity and external disturbance of the ith agent, and i∈{1,2,…,n}; α1, α2 and α3 are the parameters of the extended state observer respectively; for the scalar x, sgn(x) represents the symbolic function, as follows: where sig r (x) = sgn(x)|x| r , r is a constant; The method for designing parameters of the extended state observer in step S3 is specifically as follows: The estimation errors are defined as follows: The Lyapunov function is designed as follows: in To satisfy the positive condition, p 11 >0 The extended state observer can estimate the agent when the extended state observer parameters α1, α2, and α3 satisfy the following conditions: P1<0 k<0 α1,α2,α3>0 a1p 11 +2a2p 12 -2kp 13 >0 4(α1p 11 +2α2p 12 -2kp 13 )p 12 +(p 11 -α1p 13 -2α2p 22 +2kp 23 ) 2 <0 At the same time, the position estimation error satisfies M>0; The consistency control protocol designed in step S4 is as follows: where u(t)=[u1(t),…,u n (t)] T ,x(t)=[x1(t),…,x n (t)] T ,v(t)=[v1(t),…,v n (t)] T , L is the Laplace matrix of the multi-agent system, which represents the communication relationship between agents. The specific expression is as follows: where a ij is an element of the adjacency matrix A; when agent i can send information to agent j, then a ij =1, otherwise a ij =0.

2. According to claim 1, a second-order multi-agent system consensus control method based on an extended state observer is characterized in that: In step S5, a test is performed based on a MATLAB / SIMULINK simulation platform to obtain the position and speed change curves in the multi-agent system, and the curves are compared with the change curves without using an extended state observer to verify the system performance.

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